SocKult analysis
Stan code for the analysis of my Social and Cultural Dynamics exam
Plate notation
stan code
## //modell
## data{
## // number of data points, groups, and vowels
## int<lower=1> N;
## int<lower=1> N_group;
## int<lower=1> N_vowel;
##
## // binomial data for the two psychometric functions
## int k_ind[N];
## int k_gro[N];
## int n_ind[N];
## int n_gro[N];
##
## // input data
## int group[N];
## int intensity[N];
## int vowel[N];
##
##
## // collective benefit model
## real local_confidence[N_group];
##
## }
##
##
## parameters{
##
## // less important note: I tried two different parametrisations of the random slope-intercept covariance,
## // and couldn't get the cholesky decomposition to work
## // ==================================
## // Option 1) specify var-covar matrices manually
## vector[2] gv_group[N_group];
## vector[2] gv_vowel[N_vowel];
## vector[2] iv_group[N_group];
## vector[2] iv_vowel[N_vowel];
##
## corr_matrix[2] gRho_group;
## corr_matrix[2] gRho_vowel;
## corr_matrix[2] iRho_group;
## corr_matrix[2] iRho_vowel;
##
##
##
## // =========================================
## // Option 2: cholesky decomposition
## // cholesky_factor_corr[2] gL_group;
## // vector<lower=0>[2] gcsigma_group;
## // cholesky_factor_corr[2] gL_vowel;
## // vector<lower=0>[2] gcsigma_vowel;
## //
## // cholesky_factor_corr[2] iL_group;
## // vector<lower=0>[2] icsigma_group;
## // cholesky_factor_corr[2] iL_vowel;
## // vector<lower=0>[2] icsigma_vowel;
##
##
## // scale parameters for the random effects
## vector<lower=0>[2] gsigma_group;
## vector<lower=0>[2] gsigma_vowel;
## vector<lower=0>[2] isigma_group;
## vector<lower=0>[2] isigma_vowel;
##
## // main effects
## real ga;
## real gb;
## real ia;
## real ib;
##
##
## // =========================================================
## // parameters for the collective benefit model
## // real collective_mu;
## real<lower=0> collective_sigma;
## //
## real col_a;
## real col_b_confidence;
##
##
## }
## transformed parameters{
## real<lower=0> collective_benefit[N_group];
## for ( k in 1:N_group ) {
## collective_benefit[k] = inv_logit(
## gv_group[k,2] * gsigma_group[2])
## / inv_logit(
## iv_group[k,2] * isigma_group[2]);
## // collective_benefit[i] = inv_logit(gb) - inv_logit(ib);
## }
##
## }
##
##
## model{
##
## // logit(theta) = A + B * data
## vector[N] gtheta;
## vector[N] gA;
## vector[N] gB;
##
## vector[N] itheta;
## vector[N] iA;
## vector[N] iB;
##
## real collective_mu[N];
##
## ia ~ normal(0, 1);
## ib ~ normal(0, 1);
## ga ~ normal(0, 1);
## gb ~ normal(0, 1);
##
##
## // scale of the random effects
## gsigma_group ~ cauchy( 0 , 2 );
## gsigma_vowel ~ cauchy( 0 , 2 );
## isigma_group ~ cauchy( 0 , 2 );
## isigma_vowel ~ cauchy( 0 , 2 );
##
##
##
## // ==================================
## // 1) specify var-covar matrices manually
## // correlations of the random effects
## gv_group ~ multi_normal(rep_vector(0,2), gRho_group);
## gv_vowel ~ multi_normal(rep_vector(0,2), gRho_vowel);
## iv_group ~ multi_normal(rep_vector(0,2), iRho_group);
## iv_vowel ~ multi_normal(rep_vector(0,2), iRho_vowel);
##
##
## gRho_group ~ lkj_corr( 4 );
## gRho_vowel ~ lkj_corr( 4 );
## iRho_group ~ lkj_corr( 4 );
## iRho_vowel ~ lkj_corr( 4 );
##
##
##
## // =========================================
## // 2: cholesky decomposition
## // cholesky stuff - gives me high Rhat and constant L=1
## // gv_group ~ multi_normal_cholesky( rep_vector(0,2) , diag_pre_multiply(gcsigma_group, gL_group));
## // gv_vowel ~ multi_normal_cholesky( rep_vector(0,2) , diag_pre_multiply(gcsigma_vowel, gL_vowel));
## // gcsigma_vowel ~ cauchy(0,2);
## // gcsigma_group ~ cauchy(0,2);
## // gL_group ~ lkj_corr_cholesky(4);
## // gL_vowel ~ lkj_corr_cholesky(4);
## //
## // iv_group ~ multi_normal_cholesky( rep_vector(0,2) , diag_pre_multiply(icsigma_group, iL_group));
## // iv_vowel ~ multi_normal_cholesky( rep_vector(0,2) , diag_pre_multiply(icsigma_vowel, iL_vowel));
## // icsigma_vowel ~ cauchy(0,2);
## // icsigma_group ~ cauchy(0,2);
## // iL_group ~ lkj_corr_cholesky(4);
## // iL_vowel ~ lkj_corr_cholesky(4);
##
##
##
##
##
## // psychometric function for both individuals and groups
## for ( i in 1:N ) {
## gA[i] = ga + gv_vowel[vowel[i],1] * gsigma_vowel[1] + gv_group[group[i],1] * gsigma_group[1];
## gB[i] = gb + gv_vowel[vowel[i],2] * gsigma_vowel[2] + gv_group[group[i],2] * gsigma_group[2];
## gtheta[i] = gA[i] + gB[i] * intensity[i];
##
## iA[i] = ia + iv_vowel[vowel[i],1] * isigma_vowel[1] + iv_group[group[i],1] * isigma_group[1];
## iB[i] = gb + iv_vowel[vowel[i],2] * isigma_vowel[2] + iv_group[group[i],2] * isigma_group[2];
## itheta[i] = iA[i] + iB[i] * intensity[i];
## }
## k_gro ~ binomial_logit(n_gro, gtheta);
## k_ind ~ binomial_logit(n_ind, itheta);
##
##
##
## // here comes the collective benefit stuff
## // not sure if I should do something something with a jacobian b/c of sampling a transformed parameter
##
## for ( k in 1:N_group ) {
## // collective_mu[k] = col_a + col_b_confidence * local_confidence[k];
## collective_benefit[k] ~ normal(col_a, 1 );
## }
##
## col_a ~ normal(1,1);
## // col_b_confidence ~ normal(0,1);
## // collective_sigma ~ cauchy(0,2);
##
## // collective_benefit[k] ~ normal(1, 1);
## // collective_benefit[k] ~ gamma(3, 2);
##
##
##
## // generated quantities{
## }
## // // =========================================
## // // 2: cholesky decomposition
## // // transform cholesky stuff back to var-covar matrixes
## // matrix[2,2] gO_group;
## // matrix[2,2] gSigma_group;
## // matrix[2,2] gO_vowel;
## // matrix[2,2] gSigma_vowel;
## // matrix[2,2] iO_group;
## // matrix[2,2] iSigma_group;
## // matrix[2,2] iO_vowel;
## // matrix[2,2] iSigma_vowel;
## //
## // gO_group = multiply_lower_tri_self_transpose(gL_group);
## // gSigma_group = quad_form_diag(gO_group, gcsigma_group);
## // gO_vowel = multiply_lower_tri_self_transpose(gL_vowel);
## // gSigma_vowel = quad_form_diag(gO_vowel, gcsigma_vowel);
## //
## // iO_group = multiply_lower_tri_self_transpose(iL_group);
## // iSigma_group = quad_form_diag(iO_group, icsigma_group);
## // iO_vowel = multiply_lower_tri_self_transpose(iL_vowel);
## // iSigma_vowel = quad_form_diag(iO_vowel, icsigma_vowel);
## // }
## Inference for Stan model: model.
## 4 chains, each with iter=10000; warmup=5000; thin=1;
## post-warmup draws per chain=5000, total post-warmup draws=20000.
##
## mean se_mean sd 2.5%
## gv_group[1,1] -5.800000e-01 0.02 0.81 -2.150000e+00
## gv_group[1,2] -1.800000e-01 0.02 0.46 -1.100000e+00
## gv_group[2,1] 7.600000e-01 0.03 0.82 -9.900000e-01
## gv_group[2,2] -8.100000e-01 0.02 0.48 -1.830000e+00
## gv_group[3,1] -1.190000e+00 0.03 0.88 -2.810000e+00
## gv_group[3,2] 5.100000e-01 0.02 0.56 -5.000000e-01
## gv_group[4,1] -2.400000e-01 0.02 0.76 -1.700000e+00
## gv_group[4,2] 5.800000e-01 0.02 0.48 -2.800000e-01
## gv_group[5,1] 3.000000e-02 0.02 0.76 -1.450000e+00
## gv_group[5,2] 8.700000e-01 0.02 0.51 -7.000000e-02
## gv_group[6,1] 2.300000e-01 0.02 0.84 -1.550000e+00
## gv_group[6,2] -1.080000e+00 0.02 0.52 -2.150000e+00
## gv_group[7,1] 1.700000e-01 0.02 0.77 -1.370000e+00
## gv_group[7,2] -3.700000e-01 0.02 0.44 -1.270000e+00
## gv_group[8,1] -8.000000e-02 0.02 0.80 -1.650000e+00
## gv_group[8,2] 1.390000e+00 0.02 0.57 3.500000e-01
## gv_group[9,1] 2.500000e-01 0.02 0.86 -1.510000e+00
## gv_group[9,2] -7.300000e-01 0.02 0.49 -1.770000e+00
## gv_vowel[1,1] 2.400000e-01 0.03 0.58 -7.100000e-01
## gv_vowel[1,2] 8.000000e-02 0.02 0.43 -7.800000e-01
## gv_vowel[2,1] -1.100000e+00 0.02 0.52 -2.250000e+00
## gv_vowel[2,2] 9.900000e-01 0.02 0.59 6.000000e-02
## gv_vowel[3,1] 2.800000e-01 0.02 0.58 -6.900000e-01
## gv_vowel[3,2] -1.030000e+00 0.02 0.56 -2.310000e+00
## gv_vowel[4,1] -1.110000e+00 0.01 0.50 -2.210000e+00
## gv_vowel[4,2] 3.000000e-01 0.02 0.45 -5.000000e-01
## iv_group[1,1] -1.200000e-01 0.03 0.86 -1.780000e+00
## iv_group[1,2] -8.200000e-01 0.02 0.56 -1.920000e+00
## iv_group[2,1] 3.400000e-01 0.03 0.93 -1.500000e+00
## iv_group[2,2] -1.180000e+00 0.02 0.62 -2.460000e+00
## iv_group[3,1] -2.600000e-01 0.02 0.80 -1.790000e+00
## iv_group[3,2] 1.000000e-01 0.02 0.62 -1.150000e+00
## iv_group[4,1] -5.800000e-01 0.03 0.89 -2.360000e+00
## iv_group[4,2] 9.600000e-01 0.02 0.68 -3.100000e-01
## iv_group[5,1] 3.500000e-01 0.02 0.80 -1.320000e+00
## iv_group[5,2] 6.400000e-01 0.02 0.62 -5.600000e-01
## iv_group[6,1] -3.200000e-01 0.02 0.85 -2.000000e+00
## iv_group[6,2] -1.200000e-01 0.02 0.66 -1.410000e+00
## iv_group[7,1] -1.600000e-01 0.02 0.81 -1.690000e+00
## iv_group[7,2] -3.000000e-01 0.02 0.58 -1.400000e+00
## iv_group[8,1] 6.700000e-01 0.02 0.85 -1.110000e+00
## iv_group[8,2] 9.200000e-01 0.02 0.72 -4.700000e-01
## iv_group[9,1] -4.800000e-01 0.03 0.88 -2.190000e+00
## iv_group[9,2] -1.600000e-01 0.02 0.65 -1.420000e+00
## iv_vowel[1,1] 4.000000e-01 0.02 0.75 -9.300000e-01
## iv_vowel[1,2] 2.900000e-01 0.03 0.75 -1.210000e+00
## iv_vowel[2,1] -6.300000e-01 0.02 0.76 -2.100000e+00
## iv_vowel[2,2] 6.600000e-01 0.02 0.71 -6.500000e-01
## iv_vowel[3,1] -9.000000e-02 0.02 0.74 -1.470000e+00
## iv_vowel[3,2] -3.800000e-01 0.02 0.67 -1.730000e+00
## iv_vowel[4,1] -5.300000e-01 0.02 0.77 -2.010000e+00
## iv_vowel[4,2] -5.500000e-01 0.02 0.71 -2.040000e+00
## gRho_group[1,1] 1.000000e+00 0.00 0.00 1.000000e+00
## gRho_group[1,2] -2.300000e-01 0.01 0.32 -7.600000e-01
## gRho_group[2,1] -2.300000e-01 0.01 0.32 -7.600000e-01
## gRho_group[2,2] 1.000000e+00 0.00 0.00 1.000000e+00
## gRho_vowel[1,1] 1.000000e+00 0.00 0.00 1.000000e+00
## gRho_vowel[1,2] -1.800000e-01 0.01 0.31 -7.300000e-01
## gRho_vowel[2,1] -1.800000e-01 0.01 0.31 -7.300000e-01
## gRho_vowel[2,2] 1.000000e+00 0.00 0.00 1.000000e+00
## iRho_group[1,1] 1.000000e+00 0.00 0.00 1.000000e+00
## iRho_group[1,2] -1.300000e-01 0.01 0.34 -7.300000e-01
## iRho_group[2,1] -1.300000e-01 0.01 0.34 -7.300000e-01
## iRho_group[2,2] 1.000000e+00 0.00 0.00 1.000000e+00
## iRho_vowel[1,1] 1.000000e+00 0.00 0.00 1.000000e+00
## iRho_vowel[1,2] -5.000000e-02 0.01 0.33 -6.500000e-01
## iRho_vowel[2,1] -5.000000e-02 0.01 0.33 -6.500000e-01
## iRho_vowel[2,2] 1.000000e+00 0.00 0.00 1.000000e+00
## gsigma_group[1] 4.900000e-01 0.01 0.31 3.000000e-02
## gsigma_group[2] 8.000000e-02 0.00 0.03 4.000000e-02
## gsigma_vowel[1] 1.620000e+00 0.04 0.91 5.800000e-01
## gsigma_vowel[2] 1.100000e-01 0.00 0.06 4.000000e-02
## isigma_group[1] 4.600000e-01 0.01 0.32 3.000000e-02
## isigma_group[2] 6.000000e-02 0.00 0.02 2.000000e-02
## isigma_vowel[1] 6.600000e-01 0.02 0.59 5.000000e-02
## isigma_vowel[2] 6.000000e-02 0.00 0.05 1.000000e-02
## ga -1.250000e+00 0.03 0.74 -2.450000e+00
## gb 1.800000e-01 0.00 0.03 1.200000e-01
## ia -1.550000e+00 0.02 0.48 -2.320000e+00
## ib -4.000000e-02 0.03 1.01 -2.030000e+00
## collective_sigma 9.179058e+307 Inf Inf 5.119840e+306
## col_a 1.000000e+00 0.01 0.32 3.800000e-01
## col_b_confidence -1.281625e+04 10352.36 19806.72 -5.791971e+04
## collective_benefit[1] 1.020000e+00 0.00 0.02 9.700000e-01
## collective_benefit[2] 1.000000e+00 0.00 0.03 9.500000e-01
## collective_benefit[3] 1.020000e+00 0.00 0.03 9.700000e-01
## collective_benefit[4] 9.900000e-01 0.00 0.03 9.400000e-01
## collective_benefit[5] 1.020000e+00 0.00 0.02 9.700000e-01
## collective_benefit[6] 9.600000e-01 0.00 0.03 9.100000e-01
## collective_benefit[7] 9.900000e-01 0.00 0.02 9.500000e-01
## collective_benefit[8] 1.030000e+00 0.00 0.03 9.800000e-01
## collective_benefit[9] 9.800000e-01 0.00 0.02 9.200000e-01
## lp__ -3.909000e+02 0.30 8.41 -4.077200e+02
## 25% 50% 75%
## gv_group[1,1] -1.100000e+00 -6.000000e-01 -7.00000e-02
## gv_group[1,2] -4.900000e-01 -1.900000e-01 1.10000e-01
## gv_group[2,1] 2.500000e-01 7.800000e-01 1.31000e+00
## gv_group[2,2] -1.120000e+00 -7.900000e-01 -4.90000e-01
## gv_group[3,1] -1.780000e+00 -1.230000e+00 -6.70000e-01
## gv_group[3,2] 1.200000e-01 4.700000e-01 8.70000e-01
## gv_group[4,1] -7.400000e-01 -2.700000e-01 2.30000e-01
## gv_group[4,2] 2.500000e-01 5.500000e-01 8.70000e-01
## gv_group[5,1] -4.500000e-01 1.000000e-02 5.10000e-01
## gv_group[5,2] 5.300000e-01 8.400000e-01 1.20000e+00
## gv_group[6,1] -3.100000e-01 2.400000e-01 7.90000e-01
## gv_group[6,2] -1.410000e+00 -1.050000e+00 -7.20000e-01
## gv_group[7,1] -3.300000e-01 1.800000e-01 6.80000e-01
## gv_group[7,2] -6.500000e-01 -3.600000e-01 -7.00000e-02
## gv_group[8,1] -5.700000e-01 -1.100000e-01 4.10000e-01
## gv_group[8,2] 9.900000e-01 1.360000e+00 1.75000e+00
## gv_group[9,1] -3.100000e-01 2.600000e-01 8.10000e-01
## gv_group[9,2] -1.030000e+00 -7.100000e-01 -4.00000e-01
## gv_vowel[1,1] -1.700000e-01 1.600000e-01 6.00000e-01
## gv_vowel[1,2] -1.900000e-01 6.000000e-02 3.30000e-01
## gv_vowel[2,1] -1.400000e+00 -1.060000e+00 -7.40000e-01
## gv_vowel[2,2] 5.600000e-01 9.200000e-01 1.34000e+00
## gv_vowel[3,1] -1.400000e-01 2.100000e-01 6.30000e-01
## gv_vowel[3,2] -1.370000e+00 -9.700000e-01 -6.20000e-01
## gv_vowel[4,1] -1.410000e+00 -1.070000e+00 -7.50000e-01
## gv_vowel[4,2] 1.000000e-02 2.700000e-01 5.60000e-01
## iv_group[1,1] -6.800000e-01 -1.300000e-01 4.50000e-01
## iv_group[1,2] -1.180000e+00 -8.100000e-01 -4.50000e-01
## iv_group[2,1] -2.800000e-01 3.600000e-01 9.80000e-01
## iv_group[2,2] -1.580000e+00 -1.150000e+00 -7.60000e-01
## iv_group[3,1] -7.900000e-01 -2.800000e-01 2.80000e-01
## iv_group[3,2] -3.000000e-01 1.000000e-01 4.90000e-01
## iv_group[4,1] -1.160000e+00 -5.900000e-01 -3.00000e-02
## iv_group[4,2] 5.100000e-01 9.200000e-01 1.39000e+00
## iv_group[5,1] -1.500000e-01 3.800000e-01 8.80000e-01
## iv_group[5,2] 2.400000e-01 6.300000e-01 1.04000e+00
## iv_group[6,1] -8.800000e-01 -3.200000e-01 2.30000e-01
## iv_group[6,2] -5.400000e-01 -1.500000e-01 2.90000e-01
## iv_group[7,1] -7.000000e-01 -1.800000e-01 3.50000e-01
## iv_group[7,2] -6.700000e-01 -3.000000e-01 6.00000e-02
## iv_group[8,1] 1.500000e-01 6.900000e-01 1.22000e+00
## iv_group[8,2] 4.500000e-01 9.200000e-01 1.39000e+00
## iv_group[9,1] -1.050000e+00 -4.900000e-01 1.00000e-01
## iv_group[9,2] -5.800000e-01 -1.800000e-01 2.40000e-01
## iv_vowel[1,1] -1.300000e-01 3.500000e-01 8.70000e-01
## iv_vowel[1,2] -1.700000e-01 2.600000e-01 7.50000e-01
## iv_vowel[2,1] -1.110000e+00 -6.400000e-01 -1.60000e-01
## iv_vowel[2,2] 1.900000e-01 6.000000e-01 1.10000e+00
## iv_vowel[3,1] -5.700000e-01 -1.300000e-01 3.60000e-01
## iv_vowel[3,2] -7.900000e-01 -3.700000e-01 4.00000e-02
## iv_vowel[4,1] -1.020000e+00 -5.400000e-01 -7.00000e-02
## iv_vowel[4,2] -9.900000e-01 -5.300000e-01 -1.10000e-01
## gRho_group[1,1] 1.000000e+00 1.000000e+00 1.00000e+00
## gRho_group[1,2] -4.600000e-01 -2.600000e-01 -1.00000e-02
## gRho_group[2,1] -4.600000e-01 -2.600000e-01 -1.00000e-02
## gRho_group[2,2] 1.000000e+00 1.000000e+00 1.00000e+00
## gRho_vowel[1,1] 1.000000e+00 1.000000e+00 1.00000e+00
## gRho_vowel[1,2] -4.000000e-01 -2.000000e-01 3.00000e-02
## gRho_vowel[2,1] -4.000000e-01 -2.000000e-01 3.00000e-02
## gRho_vowel[2,2] 1.000000e+00 1.000000e+00 1.00000e+00
## iRho_group[1,1] 1.000000e+00 1.000000e+00 1.00000e+00
## iRho_group[1,2] -3.900000e-01 -1.500000e-01 1.10000e-01
## iRho_group[2,1] -3.900000e-01 -1.500000e-01 1.10000e-01
## iRho_group[2,2] 1.000000e+00 1.000000e+00 1.00000e+00
## iRho_vowel[1,1] 1.000000e+00 1.000000e+00 1.00000e+00
## iRho_vowel[1,2] -2.900000e-01 -6.000000e-02 1.80000e-01
## iRho_vowel[2,1] -2.900000e-01 -6.000000e-02 1.80000e-01
## iRho_vowel[2,2] 1.000000e+00 1.000000e+00 1.00000e+00
## gsigma_group[1] 2.500000e-01 4.500000e-01 6.60000e-01
## gsigma_group[2] 6.000000e-02 7.000000e-02 9.00000e-02
## gsigma_vowel[1] 1.000000e+00 1.380000e+00 1.99000e+00
## gsigma_vowel[2] 7.000000e-02 9.000000e-02 1.30000e-01
## isigma_group[1] 2.100000e-01 4.000000e-01 6.30000e-01
## isigma_group[2] 4.000000e-02 5.000000e-02 7.00000e-02
## isigma_vowel[1] 2.800000e-01 5.100000e-01 8.50000e-01
## isigma_vowel[2] 3.000000e-02 5.000000e-02 7.00000e-02
## ga -1.770000e+00 -1.340000e+00 -8.10000e-01
## gb 1.600000e-01 1.800000e-01 2.00000e-01
## ia -1.860000e+00 -1.610000e+00 -1.32000e+00
## ib -7.100000e-01 -4.000000e-02 6.50000e-01
## collective_sigma 4.688335e+307 9.308606e+307 1.36593e+308
## col_a 7.700000e-01 9.900000e-01 1.21000e+00
## col_b_confidence -2.938946e+04 -2.245370e+03 2.02157e+03
## collective_benefit[1] 1.000000e+00 1.020000e+00 1.03000e+00
## collective_benefit[2] 9.800000e-01 1.000000e+00 1.02000e+00
## collective_benefit[3] 1.000000e+00 1.020000e+00 1.03000e+00
## collective_benefit[4] 9.800000e-01 1.000000e+00 1.01000e+00
## collective_benefit[5] 1.000000e+00 1.020000e+00 1.03000e+00
## collective_benefit[6] 9.500000e-01 9.600000e-01 9.80000e-01
## collective_benefit[7] 9.800000e-01 9.900000e-01 1.01000e+00
## collective_benefit[8] 1.010000e+00 1.030000e+00 1.04000e+00
## collective_benefit[9] 9.600000e-01 9.800000e-01 9.90000e-01
## lp__ -3.964900e+02 -3.908100e+02 -3.85170e+02
## 97.5% n_eff Rhat
## gv_group[1,1] 1.130000e+00 1171 1.00
## gv_group[1,2] 7.400000e-01 679 1.01
## gv_group[2,1] 2.320000e+00 725 1.01
## gv_group[2,2] 7.000000e-02 875 1.01
## gv_group[3,1] 7.000000e-01 915 1.00
## gv_group[3,2] 1.690000e+00 715 1.00
## gv_group[4,1] 1.360000e+00 1152 1.00
## gv_group[4,2] 1.610000e+00 776 1.01
## gv_group[5,1] 1.610000e+00 1167 1.00
## gv_group[5,2] 1.920000e+00 759 1.01
## gv_group[6,1] 1.860000e+00 1215 1.00
## gv_group[6,2] -1.400000e-01 952 1.00
## gv_group[7,1] 1.710000e+00 1379 1.01
## gv_group[7,2] 4.600000e-01 825 1.01
## gv_group[8,1] 1.560000e+00 1202 1.00
## gv_group[8,2] 2.570000e+00 770 1.01
## gv_group[9,1] 1.930000e+00 1249 1.00
## gv_group[9,2] 2.100000e-01 973 1.00
## gv_vowel[1,1] 1.550000e+00 544 1.01
## gv_vowel[1,2] 1.000000e+00 816 1.01
## gv_vowel[2,1] -1.900000e-01 971 1.01
## gv_vowel[2,2] 2.320000e+00 747 1.00
## gv_vowel[3,1] 1.560000e+00 568 1.01
## gv_vowel[3,2] -1.500000e-01 641 1.00
## gv_vowel[4,1] -2.400000e-01 1174 1.00
## gv_vowel[4,2] 1.300000e+00 817 1.01
## iv_group[1,1] 1.600000e+00 1171 1.00
## iv_group[1,2] 2.600000e-01 1116 1.00
## iv_group[2,1] 2.120000e+00 903 1.00
## iv_group[2,2] -2.000000e-02 1050 1.01
## iv_group[3,1] 1.350000e+00 1292 1.01
## iv_group[3,2] 1.330000e+00 1102 1.00
## iv_group[4,1] 1.250000e+00 978 1.00
## iv_group[4,2] 2.380000e+00 961 1.00
## iv_group[5,1] 1.860000e+00 1134 1.00
## iv_group[5,2] 1.890000e+00 1012 1.00
## iv_group[6,1] 1.380000e+00 1251 1.00
## iv_group[6,2] 1.260000e+00 1149 1.01
## iv_group[7,1] 1.460000e+00 1379 1.00
## iv_group[7,2] 8.900000e-01 992 1.00
## iv_group[8,1] 2.280000e+00 1222 1.00
## iv_group[8,2] 2.330000e+00 878 1.00
## iv_group[9,1] 1.270000e+00 1223 1.00
## iv_group[9,2] 1.200000e+00 994 1.00
## iv_vowel[1,1] 2.020000e+00 1099 1.00
## iv_vowel[1,2] 1.900000e+00 844 1.01
## iv_vowel[2,1] 9.500000e-01 1004 1.00
## iv_vowel[2,2] 2.180000e+00 970 1.00
## iv_vowel[3,1] 1.530000e+00 1032 1.00
## iv_vowel[3,2] 9.100000e-01 1024 1.00
## iv_vowel[4,1] 1.120000e+00 1091 1.00
## iv_vowel[4,2] 8.600000e-01 915 1.00
## gRho_group[1,1] 1.000000e+00 20000 NaN
## gRho_group[1,2] 4.500000e-01 706 1.00
## gRho_group[2,1] 4.500000e-01 706 1.00
## gRho_group[2,2] 1.000000e+00 18793 1.00
## gRho_vowel[1,1] 1.000000e+00 20000 NaN
## gRho_vowel[1,2] 4.700000e-01 1239 1.00
## gRho_vowel[2,1] 4.700000e-01 1239 1.00
## gRho_vowel[2,2] 1.000000e+00 18935 1.00
## iRho_group[1,1] 1.000000e+00 20000 NaN
## iRho_group[1,2] 5.400000e-01 860 1.00
## iRho_group[2,1] 5.400000e-01 860 1.00
## iRho_group[2,2] 1.000000e+00 18931 1.00
## iRho_vowel[1,1] 1.000000e+00 20000 NaN
## iRho_vowel[1,2] 6.100000e-01 1278 1.00
## iRho_vowel[2,1] 6.100000e-01 1278 1.00
## iRho_vowel[2,2] 1.000000e+00 18977 1.00
## gsigma_group[1] 1.200000e+00 769 1.00
## gsigma_group[2] 1.500000e-01 773 1.00
## gsigma_vowel[1] 4.000000e+00 582 1.01
## gsigma_vowel[2] 2.900000e-01 931 1.00
## isigma_group[1] 1.230000e+00 708 1.01
## isigma_group[2] 1.200000e-01 730 1.00
## isigma_vowel[1] 2.250000e+00 727 1.01
## isigma_vowel[2] 1.900000e-01 1015 1.00
## ga 4.800000e-01 499 1.01
## gb 2.500000e-01 667 1.00
## ia -4.300000e-01 576 1.01
## ib 1.950000e+00 1632 1.00
## collective_sigma 1.752902e+308 20000 NaN
## col_a 1.630000e+00 1581 1.00
## col_b_confidence 8.234410e+03 4 2.97
## collective_benefit[1] 1.060000e+00 981 1.01
## collective_benefit[2] 1.060000e+00 829 1.01
## collective_benefit[3] 1.080000e+00 836 1.00
## collective_benefit[4] 1.040000e+00 735 1.01
## collective_benefit[5] 1.060000e+00 986 1.00
## collective_benefit[6] 1.010000e+00 995 1.00
## collective_benefit[7] 1.040000e+00 919 1.01
## collective_benefit[8] 1.080000e+00 1039 1.01
## collective_benefit[9] 1.020000e+00 1025 1.00
## lp__ -3.749000e+02 784 1.00
##
## Samples were drawn using NUTS(diag_e) at Mon May 22 14:26:35 2017.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).